Is it incorrect to say, 'Give me it' ? I am told that it is and one should always say, 'Give it me'?
"Give me it" sounds very odd in Standard English, but so does "give it me". If you want to be on the safe side, I would go with "give it to me".
There are, however, dialects where "give me it" and "give it me" are acceptable or even preferred, see e.g. this BBC article:
I also found this interesting quote on Google Books, in a book titled "The Edinburgh history of the Scots language":
The construction is perfectly good: in English, you can put an indirect object before the direct object, without a preposition, as
However, I find it a bit awkward to do so when the direct object (the thing you are giving) is a small as the word "it", and would more likely say give it to me.
On the other hand, I find no problem with show me it.
The it should refer to something that is already known, as used to avoid repeating yourself. Instead of:
you could use:
You would hardly say "Give the book me", even if the special form "Give it me" is used in some places.
If both me and it could be understood by the situation, you could just say (but perhaps not write):